Faculty and graduate students in the Department of Applied and Computational Mathematics and Statistics (ACMS) are always involved in dynamic research projects that enable connections on and off campus.

The overall goal of this project is to develop three-dimensional multi-scale mathematical models and a computational toolkit for simulating thrombus formation. These models will be validated with specifically designed experiments to test predictions of thrombus development, structure, and stability. Moreover, the development of reasonable models will serve as a generator of new hypotheses that can be tested in experiments in vivo.

Many bacteria use motility described as swarming to colonize surfaces in groups that allows them to survive external stresses, including exposure to antibiotics. The main goal of this interdisciplinary project is to combine simulations using new, three-dimensional multiscale modeling environments and specifically designed experiments to study the basic coordination events of bacterial swarming, which is essential to understanding how millions of bacteria function in real environments.

The long-term goal of this project is to develop a predictive and quantitative understanding of the MT cytoskeleton and its regulation by MTBPs, which will impact fields ranging from systems biology to nanotechnology. The flexible model and tutorials developed through this project will allow researchers to develop and test specific hypotheses about the mechanisms of dynamic instability and MTBP action, which will in turn help design and direct future experiments.

Many breast cancer patients remain free of distant metastasis even without adjuvant chemotherapy. While standard histopathological tests fail to identify these good prognosis patients with adequate precision, analyses of gene expression patterns in primary tumors have resulted in successful diagnostic tests. The accelerated progression relapse test, developed by Buechler (ACMS) using whole-genome microarrays, is one such test, however it requires frozen or fresh-preserved tissue samples. The project includes development of a version of this test that can utilize the tissue source (formalin-fixed, paraffin-embedded) standard in clinical use.

The overall goal is to study and understand the behavior of the wound healing process using dynamical system and PDE model through analytical and numerical tools. This research is featured here on SIAM.org.

Pseudomonas aeruginosa is an opportunistic pathogenic bacterium that often, but not always, forms branched tendril patterns during swarming. This physical phenomena occurs only when bacteria produce rhamnolipid, which is regulated by intercellular quorum sensing signaling. Here we report upon our experimental findings of a new behavior of the bacterium P. aeruginosa, an ability to alter its local physical environment by forming and propagating high density waves of cells and rhamnolipid.

Multiscale Stochastic Model of Bruising

This project involves the development of modeling and experimental approaches to detect the nature and aging of a bruise on children, especially in abusive situations.

The goal of this project is to develop efficient and robust high order accuracy numerical methods for solving hyperbolic conservation laws, Hamilton-Jacobi equations and stiff advection-reaction-diffusion equations defined on complex domains. The methods include Weighted ENO methods, discontinuous Galerkin methods, fast sweeping methods and high order time-stepping implicit integration factor methods.

Computational Analysis of Morphogenesis

The goal of this project is to develop computational models to study the tissue patterning during Drosophila (fruit fly) embryo development. Specifically, we study the robustness of multi-protein networks which regulate the morphogen gradient formation.